Lattice QCD at Fermilab Celebrating the career of Paul Mackenzie FNAL 7-8 November 2019 The History of Lattice QCD Akira Ukawa Professor Emeritus and Fellow Center for Computational Sciences, University of Tsukuba Director Center for World Premier International Research Center Initiative JSPS v The beginning v Exploring the new frontier v Building the instrument v Getting nimble with quarks Physics v Putting them all together Algorithms Machines - 1 - The beginning - 2 - Wilson 1974 n Preprint CLNS-262 (February 1974) n Gauge theory on a space-time lattice n “Wilson loop” as order parameter n 2 Confinement for large values of coupling g0 ≫ 1 See Wilson’s Lattice 2004 talk for a personal historical account of the discovery - 3 - Cornell 1975 Grad students on 5th floor Paul Mackenzie Steve Shenker Serge Rudaz Junko Shigemitsu Belal Baaqui Michael Peskin I was on 3rd floor. Laboratory of Nuclear Studies Cornell University Faculty Ken Wilson John Kogut Tun-Mow Yan Tom Kinoshita Don Yennie Kurt Gottfried - 4 - Early reception 200 #citations/year of Wilson’s 1974 paper 150 100 50 Total citation to date : 3787 (WoS data base) 0 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 n The paper attracted much interest, but in fact, there was little progress in the first 5 years….. n strong-coupling expansion of hadron masses (Kogut et al) did not lead to anywhere n “theoretical ideas” like “duality” , “monopole condensation” (‘tHooft, Polyakov …) attracted more interest - 5 - Creutz 1979 n Preprint-79-0919(BNL)(September 1979) n Computer evaluation of Wilson loop (VAX 11/780!) 2314 n Non-zero string tensionMICHAEL for smallerCREUTZ values of the coupling consistent with asymptotic freedom IO behavior of Eq. (3.22) occurs rather sharply over a range of about 10% in P about P =2. This appear- Earlierance of forthe Z(2)confinement :Creutz-Jacobsmechanism-Rebbi, PRLoccurs 42, at1390 (1979) σ a2 Also for S(2):Wilson, Cargese Summer Institute (1979) = 0.16. (5.1) 4p l. PHYSICAL REVIEW 0 VOLUME 21, NUMBER 8 15 AP RI L 1980 o The rapid evolution out of the perturbative regime may be responsible for the remarkable phenome- Monte Carlo study of quantized SU(2) gauge theory a K nological successes of the bag model. " High- temperature-seriesMichael Creutzresults, "as well as semi- Department ofclassicalPhysics, Brookhaventreatments,National' haveLaboratory,alsoUpton,suggestedNew Yorkan11973 abrupt onset(Receivedof confinement.24 October 1979) O. I Using Monte Carlo techniques,Our analysiswe evaluate allowspath integralsa determinationfor pure SU(2) ofgaugethe fields.re- Wilson's . regularization procedure onnormalizationa lattice of up to 10'scalesites controlsof the ultravioletcouplingdivergences.in termsOurofrenormalizationthe prescription, based on confinement, is to hold fixed the string tension, the coefficient of the 4 string tension. Using the observed asymptotic asymptotic linear potential between sources in the fundamental representation of the gauge group. Upon reducing the 2 cutoff, we observe a logarithmicnormalizationdecrease of the bare coupling constant in a manner consistent with the g0 perturbative renormalization-group prediction. This supports the coexistence of confinement and asymptotic freedom for quantized non-Abelian fields. 0.0 I gauge (5.2) 0 |.O 2.0 - 6 - 4 2 eo we can solve for e,' to give FIG. 6. The cutoff squared times the string tensionI. INTRODUCTION regime. Such a transition is essential for the lat- function of The solid lines are the strong- and eo 37T as a P. ~-0 tice formulation of conventional(5.3) electrodynamics weak-coupling limits. Gauge theories currently dominate 4wour under-11 ln(1/aA)'where photons and electrons exist as free parti- standing of elementary particle'physics.where theIndeed,renormalizationcles. scale is low P =2.1 only loops of sidewe1nowand conceive2 are signifi-that all interactions represent Renormalization-group analysis implies that for cantly different from zero soramificationswe must includeof underlyingthe local symmetries. The 6m' short-distance1 phenomena the effective coupling of A=@ Kexp — = v K. (5.4) loop of side 0 in the fit. BelowelegantP =1.inclusion6 only ofthethe strong nuclear force into 11 non-Abelian200 gauge theories becomes' small and loop of side 1 is significant thisand picturewe assumedemandsthe the phenomenon of confine- perturbative results become valid. If this "as- Thus we see the appearance of a rather large di- area term C dominates. Fromment;Eq.indeed,(3.21)physicalwe iden-hadrons should be gauge- ymptotic freedom" is to arise in the confining bound of the fundamentalmensionless andnumber. The uncertaintyWilson's formulation,in this co- then four space- tify singlet states quark phase of gluon degrees of freedom. At ourefficientpresent islevelroughlyof a timefactordimensionsof two becausemust beofinadequatethe to support the knowledge, confinement(4.4)appears largeto playcoefficienta role in thetransitionexponential.of Ref.The7. Asrenor-evidence for this, Migdal solely for the unbroken non-Abelianmalizationgauge theorymass shouldhasbepresentedstrongly andependentapproximateon nonperturbative re- In Fig. 6 we summarize these results by plot- of the of strong interactions. both the gauge group andcursionadditionrelationof quarks.between different values ting a'K versus p. Here we alsoTheoreticalplot theevidencestrong- for quark confinement by cutoff parameter. ' He finds a close analogy We have shown the onset of asymptotic freedom coupling result of Eq. (3.24)gaugeand fieldsthe weak-couplingis remarkably sparse. Renormaliza- between d-dimensional gauge theories and (d/2) for the bare coupling constant in a renormaliza- conclusion of Eq. (3.22) withtion-groupan arbitrarilyargumentschosenimply that perturbation -dimensional nearest-neighbor spin systems of tion scheme 'based on confinement. This is normalization. From P =1.theory6 to 1.may8 webeplotinapplicableboth at large distances, statistical mechanics. On this basis he concludes strongly suggestive' that SU(2) non-Abelian gauge the least-square fit and the thusresultdismissingof assumingthe lack of perturbative evidence that four dimensions represents a critical case for confinement of quarks. ' Studiestheoryof largesimultaneouslyor- whereexhibitsgaugeconfinementtheories basedand on non-Abelian groups pure area-law behavior. For P =2.2 and 2.25 we ders in the weak-coupling expansion'asymptoticas well freedom.as onlyFurthermore,possess the byconfiningreproduc-phase, whereas the plot fits including and not including the loop of semiclassical treatments" all suggesting theimportantasymptotic-freedomAbelian prediction,group U(l) ofweelectrodynamics possesses side zero. Above P =2.5 the area law is too sub- nonperturbative effects in non-Abelianstrengthengauge ties betweena peculiarthe latticetransitionformulationsimilar andto that occurring in dominant relative to the perimeter law for accur- "XY" ' theories. the more conventional theperturbativetwo-dimensionalapproaches model. ate determination. As each temperature is treated Monte Carlo techniques have Any true nonperturbative analysisto gaugerequirestheory.a Recently, proven independently of the others, meansthe fluctuationsof controlling appar-the ultraviolet divergences of to be a powerful nonperturbative tool for analysis ent in this figure represent fieldthe statisticaltheory in a mannererror independent of Feynman of quantized gauge fields. "'" We have seen clear of this analysis. diagrams. Wilson's formulation of gauge theory onACKNOWLEDGMENTSconfinement-spin-wave phase transitions for U(1) a lattice provides such a cutoff scheme. ' This par- lattice gauge theory in four space-time dimensions I have benefited from many interesting dis- V. DISCUSSIONticular regulator also preserves an exact: local and for the SU(2) theory in five dimensions. " In symmetry. With the cutoff in place,cussionsWilsonwithde- B. Freedmancontrast,andthisR. transitionSwendsen. appearsThis to be absent for Note that the changeover rivedfrom athestrong-couplingstrong-coup- expansionresearchin terms wasof performedthe four-dimensionalunder Contract No.SU(2)EY-model. These results ling behavior of Eq. (3.24) toquarksthe weak-couplingconnected by strings. In 76-02-0016this picture con-with the U.supportS. Departmentthe MigdalofargumentsEnergy. on the existence of finement arises naturally; however, to take the phase transitions; however, the observation of continuum limit one must leave the strong-coupling first-order transitions in Z„Z„and Z, lattice domain and the expansion could fail to converge. gauge theories rather than the predicted second- Balian, Drouffe, and Itzykson have presented ar- order critical points shows that Migdal's approxi- D. Gross and F. Wilczek, Phys.gumentsRev. Lett.that in30,a 1346sufficient numberM.ofBoth,space-timePhys. Bev. Lett.mate36,recursion768 (1976);relations36, 1161(E)may misidentify the na- {1973); Phys. Rev. D 8, 3633dimensions,(1973); H. D.thePolitzer,lattice theory will (1976);exhibit Y.a phaseP. Yao, ibid.ture36,of653the(1976);transition.T. Appelquist," Phys. Bev. Lett. 30, 1343 (1973).transition between the strong-couplingM. Dine,regionandofI. Muzinich, InPhys.this paperLett. we69B,extend231 (1977).our analysis of the four- 2T. Appelquist, J. Carazzone, confinementH. Kluberg-Stern,and theandweak-coupling L.perturbativeN. Lipatov, Zh. Eksp.dimensionalTeor. Fiz. SU(2)Pis'matheory.Bed. 25,Working on lattices of 21 2808 VOLUME 47, NUMBER 25HamberPHYSICAL REVIEW -LETTERSParisi21 DECEMBER, Weingarten1981 1981 data for m between 0.3